Find all real solutions to $x^4+(2-x)^4=34$.  Enter all the solutions, separated by commas.
Let $y = x - 1.$  Then $x = y + 1,$ and
\[(y + 1)^4 + (-y + 1)^4 = 34.\]Expanding, we get $2y^4 + 12y^2 - 32 = 0.$  This factors as $2(y^2 - 2)(y^2 + 8) = 0,$ so $y = \pm \sqrt{2}.$  Thus, the solutions in $x$ are $\boxed{1 + \sqrt{2}, 1 - \sqrt{2}}.$